A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation: Multiple exp-function algorithm; conservation laws; similarity solutions
A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–...
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| Published in: | Communications in nonlinear science & numerical simulation Vol. 106; p. 106072 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Amsterdam
Elsevier B.V
01.03.2022
Elsevier Science Ltd |
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| ISSN: | 1007-5704, 1878-7274 |
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| Abstract | A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–Petviashvili equation is ambassador of the higher dimensional Kadomtsev–Petviashvili hierarchy. This equation was acquired by a diminution for the well-known three-dimensional Kadomtsev–Petviashvili equation which illustrates the dissemination of nonlinear waves in plasmas and fluid dynamics. We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method. Finally, we compute conserved currents courtesy using the invariance and multiplier technique. The findings can well mimic complex waves and their dealing dynamics in fluids.
•A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed.•We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method.•Finally, we compute conserved currents courtesy using the invariance and multiplier technique.•The Lie point symmetries consist of time translation, space translation and a scaling transformation.•The novell similarity reductions and new exact solutions are computed. The solutions obtained include the solitary waves, cnoidal and snoidal waves.•In addition, we derive the conservation laws of the underlying system by employing the multiplier variational method and discuss the significance of the computed conservation laws. |
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| AbstractList | A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–Petviashvili equation is ambassador of the higher dimensional Kadomtsev–Petviashvili hierarchy. This equation was acquired by a diminution for the well-known three-dimensional Kadomtsev–Petviashvili equation which illustrates the dissemination of nonlinear waves in plasmas and fluid dynamics. We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method. Finally, we compute conserved currents courtesy using the invariance and multiplier technique. The findings can well mimic complex waves and their dealing dynamics in fluids.
•A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed.•We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method.•Finally, we compute conserved currents courtesy using the invariance and multiplier technique.•The Lie point symmetries consist of time translation, space translation and a scaling transformation.•The novell similarity reductions and new exact solutions are computed. The solutions obtained include the solitary waves, cnoidal and snoidal waves.•In addition, we derive the conservation laws of the underlying system by employing the multiplier variational method and discuss the significance of the computed conservation laws. A generalized (1 + 2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation which is an augmentation of the Bogoyavlenskii–Schiff equation and Kadomtsev–Petviashvili equation is probed. This equation is hired as a prototype for evolutionary shallow-water waves. The Bogoyavlenskii–Kadomtsev–Petviashvili equation is ambassador of the higher dimensional Kadomtsev–Petviashvili hierarchy. This equation was acquired by a diminution for the well-known three-dimensional Kadomtsev–Petviashvili equation which illustrates the dissemination of nonlinear waves in plasmas and fluid dynamics. We determine novel exact solutions by utilizing the multiple exp-function algorithm and the modern group analysis method. Finally, we compute conserved currents courtesy using the invariance and multiplier technique. The findings can well mimic complex waves and their dealing dynamics in fluids. |
| ArticleNumber | 106072 |
| Author | Adem, A.R. Muatjetjeja, B. Moretlo, T.S. |
| Author_xml | – sequence: 1 givenname: T.S. surname: Moretlo fullname: Moretlo, T.S. email: thabo.moretlo@spu.ac.za organization: Department of Mathematical Sciences, Sol Plaatje University, Private Bag X5008, Kimberley 8300, Republic of South Africa – sequence: 2 givenname: A.R. surname: Adem fullname: Adem, A.R. email: ademar@unisa.ac.za organization: Department of Mathematical Sciences, University of South Africa, UNISA 0003, Republic of South Africa – sequence: 3 givenname: B. surname: Muatjetjeja fullname: Muatjetjeja, B. email: muatjetjejab@ub.ac.bw organization: Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana |
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| Keywords | Multiple exp-function algorithm Conservation laws 35C05 35G20 Similarity solutions A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation 35C07 |
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| SubjectTerms | A generalized ([formula omitted])-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation Algorithms Conservation laws Exact solutions Fluid dynamics Multiple exp-function algorithm Nonlinear equations Plasmas (physics) Schrodinger equation Similarity solutions Water waves |
| Title | A generalized (1+2)-dimensional Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation: Multiple exp-function algorithm; conservation laws; similarity solutions |
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